Multiple Traveling Salesman Problem (MTSP) is an important combinatorial optimization problem. However, it is applicable to only the cases in which multiple executing individuals (traveling salesman) share the common workspace (city set). It cannot be used to handle many multi-machine engineering systems where multiple machines’ workspaces are not the same and partially overlap with each other....

Parallel genetic algorithms (PGAs) have been developed to reduce the large execution times that are associated with serial genetic algorithms (SGAs). They have also been used to solve larger problems and to find better solutions. In this paper, a comparative analysis of five different coarse-grained PGAs is conducted using the traveling salesman problem as the basis of this case study. To make ...

In this work we investigate two variants of the Stochastic Vehicle Routing Problem: The Vehicle Routing Problem with Stochastic Demands and the Vehicle Routing Problem with Stochastic Demands and Customers. We show that under some moderate conditions there is an asymptotic equivalence between the Vehicle Routing Problem with Stochastic Demands and the Traveling Salesman Problem, as well as betw...

When the matrix of distances between cities is symmetric and circulant, the traveling salesman problem (TSP) reduces to the so-called symmetric circulant traveling salesman problem (SCTSP), that has applications in the design of reconfigurable networks, and in minimizing wallpaper waste. The complexity of the SCTSP is open, but conjectured to be NP-hard, and we compare different lower bounds on...

In the quadratic traveling salesman problem a cost is associated with any three nodes traversed in succession. This structure arises, e. g., if the succession of two edges represents energetic conformations, a change of direction or a possible change of transportation means. In the symmetric case, costs do not depend on the direction of traversal. We study the polyhedral structure of a lineariz...

The Single Machine Scheduling with Changeover Costs problem is found in many different workshops. In this case, the main criterion is the sequence-dependent changeover-costs or setup times. This Scheduling problem can be modeled as a Traveling Salesman Problem (TSP) and when time constraints are inserted into the model such as due-dates, the resulting problem is known as the Time Dependent Trav...

The attempts to use mobile robots in a variety of environments are currently being limited by their navigational capability, thus a set of robots must be configured for one specific environment. The problem of navigating an environment is the fundamental problem in mobile robotic where various methods including exact and heuristic approaches have been proposed to solve the problem. This paper p...

In this note, we show that the Traveling Salesman Problem cannot be solved in polynomial-time on a classical computer. Disclaimer: This article was authored by Craig Alan Feinstein in his private capacity. No official support or endorsement by the U.S. Government is intended or should be inferred. Consider the following well-known NP-hard problem: Traveling Salesman Problem A traveling salesman...

The spscefilling curve (SFC) method of Bartholdy and Platzman is an extremely fast heuristic for the Euclidean Traveling Salesman Problem. The authors show how genetic search over a parametrized family of spacefilling curves can be used to improve the quality of the the tours generated by SFC. The computational effort required grows slowly as a function of problem size, and the tours obtained d...